When watching anime I heard this word come across (Tsuki ga kirei, ep4, somewhere at the end) and I was wondering if it is a combination of nani and ka or just another word. If it is a combination then why would it be used like that? with both nani and ka, which both imply a question. Alternatively, I know a word exists, which is nanika (I believe it ment: 'something'). Could it be just this word, but then the i removed. If that is the case why would it be removed? Anyway, it would be appreciated if anyone could shed some more light on this whole thing.
なんか is an informal version of 何か (なにか). So you are correct in your assumption that it is a combination of なに and か.
Interrogative words like なに (what), どこ (where), どれ (which), etc, are known as 'indeterminate pronouns' (see a related answer here), and when combined with the particle か, indicate that the object is unidentified. It generally corresponds to 'some ～' in English. Here are some more examples of か being added to indeterminate pronouns:
どちらか one of the two
いつか some day
いくつか a few
いくらか some amount